The Museum of HP Calculators

Saturnian Satellites for the HP-41

This program is supplied without representation or warranty of any kind. Jean-Marc Baillard and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

Overview

-This program calculates the coordinates x and y of the first 7 satellites of Saturn, namely:
1 = Mimas 3 = Tethys 5 = Rhea 7 = Hyperion
2 = Enceladus 4 = Dione 6 = Titan
-The x-axis coincides with the equator of the planet.
-The center of Saturn is the origin and x , y are measured in units of Saturn's equatorial radius ( the polar radius of Saturn is 0.895 ).

Data Registers: R00 thru R14 are used for temporay data storage and when the program stops:

Mimas - Enceladus - Tethys - Dione - Rhea - Titan - Hyperion

R01 = x₁ R03 = x₂ R05 = x₃ R07 = x₄ R09 = x₅ R11 = x₆ R13 = x₇
R02 = y₁ R04 = y₂ R06 = y₃ R08 = y₄ R10 = y₅ R12 = y₆ R14 = y₇

Flags:     F01 F02 F03 F04 F05 F06 F07
              -Flag nn is set when the distance Earth-Satellite n is shorter than the distance Earth-Saturn   ( 0 < nn < 8 )
Subroutine:   none if you have a Time Module
                       "J0" otherwise .( cf for instance "Phases of the Moon for the HP-41" )

The program listing

01 LBL "METDRTH"
02 DEG
03 HR
04 24
05 /
06 X<>Y
07 XEQ "J0"         if you have a Time module, replace lines 07-08 by   the 3 lines    1.012   DDAYS   -
08 +
09   E6
10 /
11 STO 00
12 985600
13 *
14 2.96
15 -
16 STO 01
17 SIN
18 1.92
19 *
20 RCL 01
21 ST+ X
22 SIN
23 50
24 /
25 +
26 STO 02
27 RCL 00
28 33444
29 *
30 43
31 -
32 STO 03
33 SIN
34 636
35 *
36 RCL 03
37 ST+ X
38 SIN
39 22
40 *
41 +
42 RCL 00
43 1116
44 *
45 7
46 -
47 SIN
48 81
49 *
50 +
51 RCL 00
52 32344
53 *
54 60
55 -
56 STO 06
57 SIN
58 23
59 *
60 -
61 RCL 00
62 34576
63 *
64 50
65 -
66 SIN
67 5
68 *
69 +
70 RCL 00
71 16172
72 *
73 76
74 -
75 SIN
76 12
77 *
78 -
79   E2
80 /
81 STO 04
82 -
83 RCL 00
84 952149
85 *
86 +
87 49.91
88 +
89 STO 05
90 1
91 RCL 01
92 ST+ 02
93 COS
94 60
95 /
96 -
97 9.57
98 RCL 03
99 COS
100 .53
101 *
102 -
103 RCL 03
104 ST+ 04
105 ST+ X
106 COS
107 68
108 /
109 -
110 RCL 06
111 COS
112 53
113 /
114 +
115 STO 06
116 X^2
117 LASTX
118 R^
119 *
120 ST+ X
121 RCL 05
122 COS
123 *
124 -
125 X<>Y
126 X^2
127 +
128 SQRT
129 STO 01
130 /
131 RCL 05
132 SIN
133 *
134 ASIN
135 RCL 05
136 +
137 RCL 02
138 -
139 23.41
140 -
141 RCL 00
142 9
143 *
144 -
145 STO 02
146 COS
147 28.05
148 STO 07
149 SIN
150 STO 05
151 *
152 RCL 04
153 30
154 RCL 00
155 *
156 +
157 20.61
158 -
159 SIN
160 23
161 /
162 RCL 06
163 *
164 RCL 01
165 /
166 ST* 05
167 RCL 07
168 COS
169 STO 03
170 *
171 +
172 X<> 02
173 1
174 P-R
175 CHS
176 RCL 03
177 *
178 RCL 05
179 +
180 X<>Y
181 R-P
182 X<>Y
183 X<> 01
184 173 E6
185 /
186 ST- 00
187 CLX                if you don't have an HP-41 CX , replace lines 187-188 by CF 01 CF 02 CF 03 CF 04 CF 05 CF 06 CF 07
188 X<> F
189 16919949                ============= position of Hyperion: lines 189 thru 376 ============
190 RCL 00
191 *
192 240.7
193 +
194 562103
195 RCL 00
196 *
197 76.9
198 -
199 STO 10
200 SIN
201 9.12
202 *
203 -
204 29.9
205 RCL 00
206 52548
207 *
208 -
209 STO 12
210 RCL 10
211 +
212 SIN
213 .23
214 *
215 -
216 RCL 10
217 RCL 12
218 -
219 SIN
220 .21
221 *
222 +
223 RCL 00
224 5657028
225 *
226 76.2
227 +
228 STO 09
229 SIN
230 9
231 /
232 +
233 RCL 10
234 RCL 09
235 -
236 SIN
237 RCL 12
238 SIN
239 +
240 11
241 /
242 -
243 RCL 09
244 ST+ X
245 SIN
246 7
247 /
248 +
249 RCL 09
250 3
251 *
252 SIN
253 RCL 09
254 RCL 10
255 +
256 SIN
257 -
258 15
259 /
260 +
261 RCL 09
262 4
263 *
264 SIN
265 25
266 /
267 +
268 STO 08
269 13.84
270 RCL 00
271 51135
272 *
273 -
274 STO 07
275 206
276 P-R
277 RCL 07
278 RCL 12
279 -
280 STO 06
281 49
282 P-R
283 X<>Y
284 ST+ T
285 RDN
286 +
287 RCL 07
288 RCL 10
289 +
290 5
291 P-R
292 X<>Y
293 ST+ T
294 RDN
295 +
296 RCL 07
297 RCL 10
298 -
299 3
300 P-R
301 X<>Y
302 ST+ T
303 RDN
304 +
305 RCL 07
306 RCL 09
307 +
308 2
309 P-R
310 X<>Y
311 ST- T
312 RDN
313 -
314 RCL 07
315 RCL 09
316 -
317 2
318 SQRT
319 P-R
320 X<>Y
321 ST+ T
322 RDN
323 +
324 R-P
325 2 E3
326 /
327 STO 13
328 RCL 08
329 ENTER^
330 R^
331 -
332 STO 11
333 SIN
334 ST+ X
335 R^
336 ST* Y
337 X^2
338 5
339 *
340 4
341 /
342 RCL 11
343 ST+ X
344 SIN
345 *
346 -
347 R-D
348 -
349 RCL 01
350 +
351 RCL 13
352 X^2
353 2
354 /
355 1
356 RCL 11
357 ST+ X
358 COS
359 -
360 *
361 RCL 11
362 COS
363 RCL 13
364 *
365 +
366 24.57
367 ST* Y
368 +
369 P-R
370 X>0?
371 SF 07
372 RCL 02
373 *
374 STO 14
375 X<>Y
376 STO 13
377 RCL 00                ============= position of Titan: lines 377 thru 420 ============
378 22576976
379 *
380 43.62
381 -
382 79
383 RCL 00
384 302
385 *
386 +
387 SIN
388 12
389 /
390 -
391 STO Y
392 RCL 06
393 -
394 STO 10
395 SIN
396 3.31
397 *
398 -
399 RCL 10
400 ST+ X
401 SIN
402 17
403 /
404 +
405 RCL 01
406 +
407 20.29
408 RCL 10
409 COS
410 .59
411 *
412 +
413 P-R
414 X>0?
415 SF 06
416 RCL 02
417 *
418 STO 12
419 X<>Y
420 STO 11
421 79690048                ============= position of Rhea: lines 421 thru 436 ============
422 RCL 00
423 *
424 27.59
425 -
426 RCL 01
427 +
428 8.75
429 P-R
430 X>0?
431 SF 05
432 RCL 02
433 *
434 STO 10
435 X<>Y
436 STO 09
437 131534932                ============= position of Dione: lines 437 thru 462 ============
438 RCL 00
439 *
440 71.19
441 +
442 5
443 RCL 00
444 84305
445 *
446 -
447 +
448 SIN
449 4
450 /
451 -
452 RCL 01
453 +
454 6.27
455 P-R
456 X>0?
457 SF 04
458 RCL 02
459 *
460 STO 08
461 X<>Y
462 STO 07
463 190697912                ============= position of Tethys: lines 463 thru 498 ============
464 RCL 00
465 *
466 53.08
467 +
468 38.6
469 RCL 00
470 13968
471 *
472 -
473 STO 03
474 SIN
475 43.4
476 *
477 RCL 03
478 3
479 *
480 SIN
481 .71
482 *
483 +
484 STO 03                     this angle is also used to compute the coordinates of Mimas.
485 21
486 /
487 -
488 RCL 01
489 +
490 4.89
491 P-R
492 X>0?
493 SF 03
494 RCL 02
495 *
496 STO 06
497 X<>Y
498 STO 05
499 262731903                ============= position of Enceladus: lines 499 thru 542 ============
500 RCL 00
501 *
502 11
503 +
504 RCL 00
505 88773
506 *
507 63
508 +
509 SIN
510 4
511 /
512 +
513 RCL 00
514 253657
515 *
516 44
517 -
518 SIN
519 5
520 /
521 +
522 49
523 RCL 00
524 337962
525 *
526 -
527 +
528 SIN
529 .55
530 *
531 -
532 RCL 01
533 +
534 3.95
535 P-R
536 X>0?
537 SF 02
538 RCL 02
539 *
540 STO 04
541 X<>Y
542 X<> 03                ============= position of Mimas: lines 542 thru 575 ============
543 70.74
544 -
545 RCL 00
546 381994499
547 *
548 +
549 78.4
550 RCL 00
551 1000772
552 *
553 -
554 +
555 STO 00
556 SIN
557 2.31
558 *
559 -
560 RCL 01
561 +
562 3.08
563 RCL 00
564 COS
565 16
566 /
567 +
568 P-R
569 X>0?
570 SF 01
571 RCL 02
572 *
573 STO 02
574 X<>Y
575 STO 01
576 END

( 909 bytes / SIZE 015 )

         STACK         INPUTS       OUTPUTS

             Y    YYYY.MNDD              y₁

             X    HH.MNSS(TT)              x₁

             L             /           -sin L_E

where L_E is the saturnicentric latitude of the Earth.
Execution time = 67s.

Example1: On 2005 July 1st at 0h12m34s TT

2005.0701 ENTER^
0.1234 XEQ "METDRTH" >>>> x₁ = 1.58 X<>Y y₁ = 1.01 and in registers R01 thru R14:

Mimas - Enceladus - Tethys - Dione - Rhea - Titan - Hyperion

x₁ = 1.58 x₂ = 2.10 x₃ = 2.25 x₄ = 0.59 x₅ = 2.12 x₆ = 6.91 x₇ = -20.00
y₁ = 1.01 y₂ = 1.24 y₃ = -1.62 y₄ = -2.32 y₅ = 3.16 y₆ = -7.23 y₇ = -5.32

-Flags F01 F02 F05 are set, whence Mimas; Enceladus and Rhea are closer to the Earth than Saturn.

Example2: Every 15 years, the Earth is approximately in the plane of the rings. For instance on 1995/09/18 at 0h20m TT we find:

x₄ = 0.00 with flag F04 set: Dione is in transit over the planet's disk
y₄ = -0.14

Notes:

-This program uses a simplified method where the inclinations of the orbits of the satellites on the equatorial plane of Saturn have been neglected.
( 1.5° - 0° - 1.9° - 0° - 0.4° - 0.3° - 0.4° from Mimas to Hyperion respectively )
-Therefore, the satellite phenomena ( occultations, transits ... etc ... ) can't always be determined with certainty.
-However, the most important perturbations have been taken into account and the satellites may usually be identified.
-y-values are less accurate than x-values.
-The coordinates of Hyperion are less accurate than the other ones.
-If you don't want to compute the position of Hyperion, replace lines 391-392-393 ( STO Y RCL 06 - ) by
16.1 RCL 00 1412 * - + and delete lines 189 thru 376

References: More complete series may be found in

A. Vienne and L. Duriez 1995 "TASS1.6: Ephemerides of the major Saturnian Satellites" Astronomy & Astrophysics 297 , 588-605
L. Duriez and A. Vienne 1997 "Theory of motion and Ephemerides of Hyperion" Astronomy & Astrophysics 324 , 366-380

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